Built on

D. B. Fairlie and D. E. Roberts, Dual Models Without Tachyons - A New Approach , unpublished Durham preprint PRINT-72-2440 (1972)
1972
Earlier work this paper cites.
PhD thesis, Durham University, 1972
D. Roberts, Mathematical Structure of Dual Amplitudes · 1972
Earlier work this paper cites.
A. M. Al-Rashed and N. Zaheer, Zeros of Stieltjes and Van Vleck polynomials and applications , Journal of Mathematical Analysis and Applications 110
Original
1985
Earlier work this paper cites.
D. J. Gross and P. F. Mende, The High-Energy Behavior of String Scattering Amplitudes , Phys. Lett. B197
1987
Earlier work this paper cites.
D. J. Gross and P. F. Mende, String Theory Beyond the Planck Scale , Nucl. Phys. B303
1988
Earlier work this paper cites.
E. Corrigan and R. Sasaki, Quantum versus classical integrability in Calogero-Moser systems , J. Phys. A35
2002
Earlier work this paper cites.
E. Witten, Perturbative gauge theory as a string theory in twistor space , Commun. Math. Phys. 252
2004
Earlier work this paper cites.
R. Roiban, M. Spradlin and A. Volovich, On the tree level S matrix of Yang-Mills theory , Phys. Rev. D70
2004
Earlier work this paper cites.
N. Berkovits, An Alternative string theory in twistor space for N=4 superYang-Mills , Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
E. Witten, Parity invariance for strings in twistor space , Adv. Theor. Math. Phys. 8
2004
Earlier work this paper cites.
D. B. Fairlie, A Coding of Real Null Four-Momenta into World-Sheet Co-ordinates , Adv. Math. Phys. 2009
Original
2009
Earlier work this paper cites.
M. Spradlin and A. Volovich, From Twistor String Theory To Recursion Relations , Phys. Rev. D80
Original
2009
Earlier work this paper cites.

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Then

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Later among the works it cites.
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2016

Scattering Equations: Real Solutions and Particles on a Line

Cachazo, Freddy, Mizera, Sebastian, Zhang, Guojun

Understand

We find $n(n-3)/2$-dimensional regions of the space of kinematic invariants, where all the solutions to the scattering equations (the core of the CHY formulation of amplitudes) for $n$ massless particles are real.

On these regions, the scattering equations are equivalent to the problem of finding stationary points of $n-3$ mutually repelling particles on a finite real interval with appropriate boundary conditions.
This identification directly implies that for each of the $(n-3)!$ possible orderings of the $n-3$ particles on the interval, there exists one stable stationary point.
Furthermore, restricting to four dimensions, we find that the separation of the solutions into $k\in \{2,3,\ldots ,n-2\}$ sectors naturally matches that of permutations of $n-3$ labels into those with $k-2$ descents.

Built on

D. B. Fairlie and D. E. Roberts, Dual Models Without Tachyons - A New Approach , unpublished Durham preprint PRINT-72-2440 (1972)
1972
Earlier work this paper cites.
PhD thesis, Durham University, 1972
D. Roberts, Mathematical Structure of Dual Amplitudes · 1972
Earlier work this paper cites.
A. M. Al-Rashed and N. Zaheer, Zeros of Stieltjes and Van Vleck polynomials and applications , Journal of Mathematical Analysis and Applications 110
Original
1985
Earlier work this paper cites.
D. J. Gross and P. F. Mende, The High-Energy Behavior of String Scattering Amplitudes , Phys. Lett. B197
1987
Earlier work this paper cites.
D. J. Gross and P. F. Mende, String Theory Beyond the Planck Scale , Nucl. Phys. B303
1988
Earlier work this paper cites.
E. Corrigan and R. Sasaki, Quantum versus classical integrability in Calogero-Moser systems , J. Phys. A35
2002
Earlier work this paper cites.
E. Witten, Perturbative gauge theory as a string theory in twistor space , Commun. Math. Phys. 252
2004
Earlier work this paper cites.
R. Roiban, M. Spradlin and A. Volovich, On the tree level S matrix of Yang-Mills theory , Phys. Rev. D70
2004
Earlier work this paper cites.
N. Berkovits, An Alternative string theory in twistor space for N=4 superYang-Mills , Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
E. Witten, Parity invariance for strings in twistor space , Adv. Theor. Math. Phys. 8
2004
Earlier work this paper cites.
D. B. Fairlie, A Coding of Real Null Four-Momenta into World-Sheet Co-ordinates , Adv. Math. Phys. 2009
Original
2009
Earlier work this paper cites.
M. Spradlin and A. Volovich, From Twistor String Theory To Recursion Relations , Phys. Rev. D80
Original
2009
Earlier work this paper cites.

Similar

Cambridge University Press, New York, NY, 2010
F. W. J. Olver, D. W. Lozier, R. F. Boisvert and C. W. Clark, eds., NIST Handbook of Mathematical Functions · 2010
Cited alongside, same era.
T. Tao and V. Vu, Random matrices: Universality of local eigenvalue statistics , Acta Mathematica 206
Original
2011
Cited alongside, same era.
Y. Makeenko and P. Olesen, The QCD scattering amplitude from area behaved Wilson loops , Phys. Lett. B709
Original
2012
Cited alongside, same era.
Cambridge University Press, 2012
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. B. Goncharov, A. Postnikov and J. Trnka, Scattering Amplitudes and the Positive Grassmannian · 2012
Cited alongside, same era.
F. Cachazo and D. Skinner, Gravity from Rational Curves in Twistor Space , Phys. Rev. Lett. 110
Original
2013
Cited alongside, same era.